Chapter 5.1, Problem 15E

To determine

To find: The MRAM sums that approximate the volume of sphere of radius $5$ .

Answer to Problem 15E

The answer is:

Number of slices, $n$	$MRA{M}_n$
10	526.217
20	524.217
40	523.762
80	523.64
160	523.609

Explanation of Solution

Given information:

The approximate the volume of sphere of radius $5$ .

  $n=10,20,40,80,\text{ and }160$

Calculation:

The surface of the sphere by revolving the graph of the function $f(x)=\sqrt{25-x^2}$ about the $x$ -axis.

The partition the interval $x\in [-5,5]$ into $n$ , subintervals of equal length $\text{Δ}x=10/n$

That used MRAM to add the cylinder volumes, one may roughly estimate the sphere's volume.

  $\pi r^{2}h=\pi {\left(\sqrt{25-m_i^2}\right)}^2\text{Δ}x$

Use the function $\pi {\left(\sqrt{25-m_i^2}\right)}^2=\pi \left(25-x^2\right)$ for $x\in [-5,5]$ in the RAM program.

Number of slices, $n$	$MRA{M}_n$
10	526.217
20	524.217
40	523.762
80	523.64
160	523.609